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arXiv · 0810.1821

Dynamics of a Completely Integrable $N$-Coupled Liénard Type Nonlinear Oscillator

R. Gladwin Pradeep·V. K. Chandrasekar·M. Senthilvelan·M. Lakshmanan
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Abstract

We present a system of $N$-coupled Liénard type nonlinear oscillators which is completely integrable and possesses explicit $N$ time-independent and $N$ time-dependent integrals. In a special case, it becomes maximally superintegrable and admits $(2N-1)$ time-independent integrals. The results are illustrated for the N=2 and arbitrary number cases. General explicit periodic (with frequency independent of amplitude) and quasiperiodic solutions as well as decaying type/frontlike solutions are presented, depending on the signs and magnitudes of the system parameters. Though the system is of a nonlinear damped type, our investigations show that it possesses a Hamiltonian structure and that under a contact transformation it is transformable to a system of uncoupled harmonic oscillators.

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R. Gladwin Pradeep, V. K. Chandrasekar, M. Senthilvelan, M. Lakshmanan. 2009-02-17. Dynamics of a Completely Integrable $N$-Coupled Liénard Type Nonlinear Oscillator. https://arxiv.org/abs/0810.1821

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